Simplify the following expression: $ k = \dfrac{-10q}{10q - 10} + 4 $
Answer: In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{10q - 10}{10q - 10}$ $ \dfrac{4}{1} \times \dfrac{10q - 10}{10q - 10} = \dfrac{40q - 40}{10q - 10} $ Therefore $ k = \dfrac{-10q}{10q - 10} + \dfrac{40q - 40}{10q - 10} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{-10q + 40q - 40}{10q - 10} $ $k = \dfrac{30q - 40}{10q - 10}$ Simplify the expression by dividing the numerator and denominator by 10: $k = \dfrac{3q - 4}{q - 1}$